On a particular day, the maximum frequency reflected from the ionosphere is 10 MHz. On another day, it was found to increase to 11 MHz. Calculate the ratio of the maximum electron densities of the ionosphere on the two days. Point out a plausible explanation for this.

Options

A. 1.21
B. 0.82
C. `0.50`
D. `0.25`

Explanation

To solve the problem, we need to calculate the ratio of the maximum electron densities of the ionosphere on two different days based on the given maximum frequencies reflected from the ionosphere.

### Step-by-Step Solution:

1. **Identify the Given Frequencies:**
- On the first day, the maximum frequency \( v_c = 10 \, \text{MHz} \).
- On the second day, the maximum frequency \( v'_c = 11 \, \text{MHz} \).

2. **Use the Relation Between Frequency and Electron Density:**
- The relationship between the critical frequency \( v_c \) and the maximum electron density \( n_{\text{max}} \) is given by the formula:
\[ v_c = 9 \sqrt{n_{\text{max}}} \]
- Rearranging this formula, we can express the maximum electron density as:
\[ n_{\text{max}} = \left( \frac{v_c}{9} \right)^2 \]

3. **Calculate Electron Densities for Both Days:**
- For the first day:
\[ n_{\text{max}} = \left( \frac{10 \, \text{MHz}}{9} \right)^2 = \left( \frac{10}{9} \right)^2 \approx 1.2346 \]
- For the second day:
\[ n'_{\text{max}} = \left( \frac{11 \, \text{MHz}}{9} \right)^2 = \left( \frac{11}{9} \right)^2 \approx 1.4040 \]

4. **Calculate the Ratio of Electron Densities:**
- The ratio of the maximum electron densities on the two days is given by:
\[ \frac{n'_{\text{max}}}{n_{\text{max}}} = \frac{n'_{\text{max}}}{n_{\text{max}}} = \frac{\left( \frac{11}{9} \right)^2}{\left( \frac{10}{9} \right)^2} = \frac{11^2}{10^2} = \frac{121}{100} = 1.21 \]

5. **Conclusion:**
- The ratio of the maximum electron densities of the ionosphere on the two days is \( 1.21 \).

6. **Plausible Explanation:**
- The variation in the maximum frequency reflected from the ionosphere indicates a change in the electron density. This can be attributed to the degree of ionization of the ionosphere, which varies from day to day due to factors such as solar activity, time of day, and atmospheric conditions.